插件磁鐵已成為近代同步輻射光源發展的最重要元件，在自由電子雷射以及第三代同步輻射光源應用上，插件磁鐵中的聚頻磁鐵長度的愈來愈長，磁間隙日趨狹小，使得磁場量測工作量大增也更困難，在霍爾探棒與線圈式量測系統外，加速器界企盼有第三種磁場量測方法加入以滿足此一需求，脈衝式導線磁場量測方法(PWM)應運而生，利用一條繃緊的導線便能夠在狹小的空間進行插件磁鐵的快速量測以增加磁鐵修整的效率。建立PWM系統並不困難，一般實驗室都會採用較細的導線，且用在較短的磁鐵上，取弦波近似以簡化問題，但實際量測時都會觀察到許多額外的奇怪碎波，使得磁常量測結果嚴重失真，其精度被受爭議，在定量應用上受到限制。本文中作者利用國家同步輻射研究中心的插件磁鐵原型，安裝上PWM系統，經過有系統的實驗，闡明這些碎波的主要來源和若干限制多半來自細導線的材質缺陷與波色散，並提出改進與解決方法:使用粗導線來降低導線缺陷所造成的影響，再利用數位信號處理(DSP)快速傅利葉轉換運算將波色散作相位補償後重建磁場原貌。實驗顯示這種方法將使PWM更可靠且更有用，對磁場真實特性的掌握接近同霍爾探棒，在積分磁場量測觀點上則更勝之。在研究過程亦了解到，弦波傳播的物理及數學模型仍有許多研究空間。

Over the last few years, the insertion devices played a key role in the development of synchrotron light sources. The applications on the free electron lasers and the third generation storage rings are getting demanding of the undulator with long length and small gaps. Such applications increase the loading and difficulty of the magnetic field measurement. Other than the existing Hall probe and coil methods used in the society of accelerator, several laboratories tried to conceive a wire- based system lately so as to speed up the magnetic field measurement on the small-gap insertion devices or long ones for efficient magnetic tuning. The pulsed wire method (PWM) is one of the candidates for these purposes. In spite of the easy setup of the system of PWM, the application limitation of this method has been raised. Generally the thin wires were used and only the short magnets were measured to reduce the dispersion effect due to the stiffness of the wires. Nevertheless, a lot of spurious signals on the string wave distorting of the real field signals were still commonly observed. In this thesis the author clarified the effects from wire imperfection and dispersion of string wave, which are deemed to the main sources of the distortion and limitations. For improvement, a strategy using thick wire instead to average out the imperfection was proposed, followed by canceling the dispersion and tracing back the normal field signal by using the fast Fourier transform calculation with the knowledge of digital signal process (DSP). The author studied a test PWM system over two prototype insertion devices of National Synchrotron Radiation Research Center (NSRRC). Detailed study showed that this method will be reliable and useful in precise measurement. The fidelity is quite close to Hall probe measurement and even outweighs it in integral field aspects. Furthermore, the study reflects that the physical and mathematical models of string wave need more efforts to explore.

Reference
Development of PWM system
1. R. W. Warren, “Limitations on the use of the pulsed–wire field measuring technique”, Nucl. Instr. and Meth., A272 (1988) 257
2. R. B. Feldman and R. W. Warren, “Fully automatic wiggler-field test and correction”, Nucl. Instr. and Meth., A296 (1990) 619-623
3. Daryl W. Preston, Roger W. Warren, “Wiggler field measurements and corrections using the pulsed wire technique”, Nucl. Instr. and Meth., A318 (1992) 794-797
4. Roger W. Warren and Daryl W. Preston, “Field measurement in pulsed microwigglers”, (13th Int. Free Electron laser Conf., Santa Fe, USA, 1991) Nucl. Instr. and Meth. A318 (1992) 818
5. J.W.J. Verschuur, Roger W. Warren, “Tuning and characterization of Twente wiggler”, Nucl. Instr. and Meth. A375 (1996) 508-510
6. O. Shahal and R. Rohatgi, “Pulsed Wire Magnetic Field Measurements on a 4.3m long wiggler”, Nucl. Instr. and Meth., A285 (1989) 299-302
7. O. Shahal , B.V. elkonin and J.S. Sokolowski, “Dispersion interference in the pulsed-wire measurement method”, Nucl. Instr. and Meth., A296 (1990) 588-591
8. S. M. Wallace, W.B. Colson, G.R. Neil, L. Harwood, “Magnetic field error measurement of the CEBAF (NIST) wiggler using the pulsed wire method”, Nucl. Instr. and Meth. (14th international FEL confer.), A331 (1993) 759-762
9. A. A. Varfolomeev et., “Undulator magnetic field measurements with the wire deflection”, Nucl. Instr. and Meth., A341 (1994) 470-472
10. A. A. Varfolomeev et. “Improved wire deflection method for magnetic field measurements in long undulators”, Nucl. Instr. and Meth., A358 (1995) ABS46-47
11. A. A. Varfolomeev et. “Wire method for magnetic field measurements in long undulators”, Nucl. Instr. and Meth., A359 (1995) 93-96
12. P.V. Bousine, S.V. Tolmachev, A. A. Varfolomeev, “Detailed analysis of pulsed-wire technique accuracy”, Nucl. Instr. and Meth., A393 (1997) 414-418
13. N.S. Osmanov, S.V. Tolmachev, A. A. Varfolomeev, “Further development of the pulsed wire technique for magnetic field and focusing strength measurements in long undulators”, Nucl. Instr. and Meth., A407 (1998) 443-447
14. Mateau Fabrice, Corlier Muriel, Faye Christian, Marcouille Oliver, “Improvements of the Pulsed-Wire Method to Measure Undulators”, MT -16 (1999), IEEE Transaction on Applied Superconductivity , vol. 10, no.1, March 2000, 1443-1446
15. K. H. Park, et al., “Improvement of te pulsed wire method for undulator magnetic-field measurement”, Rev. Scientific Instruments, V 73, No. 3, p. 1442, (2002)
16. T. C. Fan et al., Proceedings of the 2001 Particle Accelerator Conference P.2775 (2001)
17. T. C. Fan, C. S. Hwang, and C. H. Chang and Ian C. Hsu , “A systematic study on the pulsed wire system for magnetic field measurements on the long undulator with high field” Rev. Scientific Instruments, V 73, No. 3, p. 1430, (2002)

Basic theory
18. S. Rayleigh, “Theory of Sound” 1877, Dover, New York, (1945, reprint).
19. James F. Doyle, “Wave Propagation in Structures – An FFT-Based Spectral Analysis Methodology”, Springer-Verlag, (1989)
20. Karl F. Graff, “Wave Motion in Elastic Solids”, Ohio State University Press, 1975

Method of vibration
21. Alexander Temnykh, “Vibrating Wire Field- Measuring Technique”, Nuclear Instruments and Methods in Physics Research A 399 (1997)
22. Alexander Temnykh, “Vibrating wire apparatus for periodic magnetic structure measurement”, Nuclear Instruments and Methods in Physics Research A 515 (2003) 387–393

Pulse wire for alignment
23. F. Brinker, A. Hagestedt, M. Wendt, “Precision alignment of BPM’s with quadrupole magnets”, LINAC 96, p.502 (1996)

Application of PWM system
24. R. Ruland et al., “Alignment of the VISA undulator”, PAC1999, p.1390
25. G. Rawowsky et al., “Measurement and Optimization of the VISA undulator” PAC1999, p.2698
26. G. Rawowsky et al., “Magnetic measurement on an in-vacuum undulator for the NSLS X-ray ring” PAC1997, p. 3497
27. Roger Carr, Erik Johnson, George Rawowsky, Steve Lidia, “Visible–infrared self- amplified spontaneous emission amplifier free electron laser undulator”, Physical Review Special Topics – Accelerators and Beams, v. 4, 122402 (2001).
28. M. Hogan, C. Pellegrini, J. Rosenzweig, G. Travish, A.Varfolomeev, “Status of the UCLA High-Gain Infrared Free Electron laser”, PAC 95 (1995)
29. M. J. Hogan, C. Pellegrini, J. Rosenzweig, S. Anderson, P. Frigola, and A. Tremaine, C. Fortgang, D. C. Nguyen, A. Varfolomeev, A. A. Varfolomeev, Roger Carr, “Measurements of Gain Larger than 105 at 12 mm in a Self-Amplified Spontaneous-Emission Free-Electron Laser”, Phy. Rev. Lett, V.81, N0. 22 (1998)

Spectrum and phase error
30. J.M. Ortega, “Optimization of a permanent magnet undulator for free electron laser studies on the ACO storage ring”, J. Alppl. Phys., 54(9) 1983

Insertion devices used (U10 & EPU)
31. Ch. Wang et al., “The construction of a 9-pole prototype for SRRC U-10 undulator”, IEEE Transactions on Magnetics, V. 32, No. 4, 1996
32. Ch. Wang, L. H. Chang, C. H. Chang, H. H. Chen, T. C. Fan, K. T. Hsu, J. Y. Hsu, C. S. Hwang, M. C. Lin. K. T. Pan, “Conceptual Design for the SRRC Elliptically Polarizing Undulator EPU5.6. Part I: Magnetic Configuration and Merit Function Optimization”, Fifth European Particle Accelerator Conference, 1996
33. Ch. Wang, M. C. Lin, C. H. Chang, L. H. Chang, H. H. Chen, T. C. Fan, K. T. Hsu, J. Y. Hsu, C. S. Hwang, K. T. Pan, “Conceptual Design for the SRRC Elliptically Polarizing Undulator EPU5.6. Part II: Magnetic Loading and Structure Deformation”, Fifth European Particle Accelerator Conference, 1996
34. C. S. Hwang, C. H. Chang, T. C. Fan, F. Y. Lin, Ch. Wang, Shuting Yeh, H. P. Chang, K. T. Hsu, L. H. Chang, P. K. Tseng, T. M. Uen, “Performance and Characteristics of a Prototype Symmetry Hybrid Adjustable Phase Undulator”, submitted to Nuclear Instruments & Methods in Physics Research, 1997
35. T. C. Fan, C. S. Hwang, C. H. Chang, “Magnet Sorting Algorithms for a Prototype of EPU for SRRC”, PAC’97, 1997
36. C. S. Hwang, T.C. Fan, F. Y. Lin, Shuting Yeh, C. H. Chang, P. K. Tseng, “The Advance Field Measurement Method with Three-orthogonal Hall Probes for Elliptically Polarizing Undulator”, submitted to SRI 1997
37. C. H. Chang, C. S. Hwang, T. C. Fan, K. H. Chen, K.T.Pan, F. Y. Lin, Ch. Wang, L.H. Chang, H.H. Chen, M. C. Lin, Shuting Yeh, “An SRRC Elliptically Polarizing Undulator Prototype to Examine Mechanical Design Feasibility and Magnetic Field Performance”, submitted to SRI 1997
38. C. H. Chang, C. S. Hwang, T. C. Fan, J.Y. Hsu, K. T. Pan, F. Y. Lin, Ch. Wang, L.H. chang, H.H. Chen, M. C. Lin, Shuting Yeh, “Results of a Magnetic Field Tests on a SRRC Elliptically Polarizing Undulator Prototype”, MT-15, 1997
39. C.H. Chang, et al, “Optimization Design for SRRC Elliptically Polarizing Undulator”, MT-15,1997
40. C. S. Hwang, C. H. Chang, T. C. Fan, Shuting Yeh, F. Y. Lin, K.H. Chen, and J.Y.Hsu, “The Magnetic Study of a Prototype Elliptically Polarized Undulator Under Different Operational Modes”, submitted to MT-15, 1997
41. T. C. Fan, C. S. Hwang, C. H. Chang, Ch. Wang, and J.R.Chen, “Magnet Sorting Algorithms for the SRRC EPU5.6”, PAC’98, 1998
42. C.S. Hwang, Shuting Yeh, C.H. Chang, T.C. Fan, J.R. Chen, “Field Optimization Algorithm for Various Variably Polarization Undulator with Changing Phase”, PAC’98, 1998
43. C.S. Hwang, C.H.Chang, H.P. Chang, K.T. Pan , Jenny Chen, C.H. Kuo, G.Y. Hsiung, J.R. Chen, K.T. Hsu, Ch. Wang, G.H. Luo, D.J. Wang, C.C. Kuo, K.K. Lin, “The Commissioning Results of 1 M Prototype EPU5.6 in SRRC”, PAC’98, 1998
44. C.H. Chang, H.H. Chen, T.C. Fan, Jenny Chen, C.S. Hwang, M.H. Huang, K.T. Hsu, F.Y. Lin, C.D. Li, H.C. Liu,Ch. Wang, “Construction and Performance of the Elliptical Polarization Undulator EPU5.6 in SRRC”
45. C.S. Hwang, et al., “The Long Loop Coil Measurement System for the Insertion Device”, Asia Particle Accelerator Conference (APAC’98), Japan, 1998.
46. C.S. Hwang, et al., “Advanced Field-Measurement Method with Three Orthogonal Hall Probes for an Elliptically-Polarizing Undulator”, J. Synchrotron Rad. (1998). 5, 471-474.
47. C.S. Hwang, Shuting Yeh, “Various Polarization Features of a Variably Polarized Undulator with Different Phasing Modes”, Nucl. Instr. and Meth. A420 (1999)29-38.

Nonlinear Waves
48. Lenoid Slepyan, et al., “Solitary Waves in an Inextensible , Flexible , Helical Fiber”, Physical Review Letter, vol. 74, No. 14, 1995
49. Philip Rosenau, “Quasi-continuous Spatial Motion of a Mass-spring Chain ”, Physical Review Letter, vol. 74, No. 14, 1995
50. E´ric Falcon, et. Al., “Observation of Sommerfeld Precursors on a Fluid Surface”, Physical Review Letters, V91, No.6, 2003